Simple algebra is sufficient to show that all the commonly accepted, empirical susceptibility relationships exhibit power laws as functions of frequency, in the limits of both low and high frequencies. The exponents of these power law relationships are presented and it is shown that simple relationships exist between them. It is established that the Debye relationship is unique. By means of Cole-Cole presentation comparison is made between the susceptibility functions. As it has been established that in order to characterise the large bulk of experimental data on solids and liquids functions requiring two characteristic parameters are required comparison is made between the Havriliak-Negami and Dissado-Hill expressions, which are of this form, and typical experimental results. It is concluded that the latter expression is more applicable.
Simple Algebra ist ausreichend, um zu zeigen, das alle allgemein akzeptierten, empirischen Suszeptibilitatsbeziehungen Potenzgesetze in Abhangigkeit von der Frequenz sind, sowohl im Grenzfall niedriger als auch hoher Frequenzen. Die Exponenten der Potenzgesetze werden dargelegt und es wird gezeigt, das zwischen ihnen einfache Beziehungen bestehen. Es wird festgestellt, das die Debye-Beziehungen eindeutig sind. Mittels Cole-Cole-Darstellung wird ein Vergleich zwischen den Suszeptibilitatsfunktionen durchgefuhrt. Da festgestellt wurde, das zur Charakterisierung des grosen Umfangs an experimentellen Daten fur Festkorper und Flussigkeiten Funktionen notwending sind, die zwei charakteristische Parameter erfordern, wird ein Vergleich zwischen den Ausdrucken von Havriliak-Negami und Dissado-Hill, die von dieser Form sind, und typischen experimentellen Ergebnissen durchgefuhrt. Es wird angenommen, das der letztere Ausdruck fur eine Anwendung besser geeignet ist.
[1]
R. Cole,et al.
Dielectric Relaxation in Glycerol, Propylene Glycol, and n‐Propanol
,
1951
.
[2]
E. Snow,et al.
Dielectric Loss due to Impurity Cation Migration in α Quartz
,
1964
.
[3]
K. Cole,et al.
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
,
1941
.
[4]
William Feller,et al.
An Introduction to Probability Theory and Its Applications
,
1951
.
[5]
R. Hill.
Characterisation of dielectric loss in solids and liquids
,
1978,
Nature.
[6]
Raymond M. Fuoss,et al.
Electrical Properties of Solids. VIII. Dipole Moments in Polyvinyl Chloride-Diphenyl Systems*
,
1941
.
[7]
Martin Goldstein,et al.
Viscous Liquids and the Glass Transition. II. Secondary Relaxations in Glasses of Rigid Molecules
,
1970
.
[8]
Graham Williams,et al.
Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function
,
1970
.
[9]
Irene A. Stegun,et al.
Handbook of Mathematical Functions.
,
1966
.
[10]
L. Dissado,et al.
Dielectric behaviour of materials undergoing dipole alignment transitions
,
1980
.
[11]
A. K. Jonscher,et al.
A new model of dielectric loss in polymers
,
1975
.
[12]
K. Hikichi,et al.
Dielectric Dispersion of Poly-γ-benzyl-L-Glutamate
,
1964
.
[13]
R. M. Hill,et al.
Non-exponential decay in dielectrics and dynamics of correlated systems
,
1979,
Nature.
[14]
A. K. Jonscher,et al.
The ‘universal’ dielectric response
,
1977,
Nature.